"Situationship" is probably the most accurate thing to call it. Not really a romance, not a friendship, not even a typical mutual enmity. But they are SOMETHING to each other.

For my specific headcanons about them... my Doctor is very ace, so their relationship isn't very intimate at all. I can't see Kal being very physical either in a non-clinical way. Doctor's interactions toward Kal are routinely awkward, exacerbated by their own autism and Kal's standoffishness about them in general. At first, Doctor isn't sure what to make of Kal's initial hostility, but the more persistent it is, the more Doctor is inclined to return the sentiment. I wouldn't say they become outright antagonistic, but a mutual distrust essentially becomes the foundation between them, despite working together for both Rhodes and Amiya's sake.

Both of them are also incredibly emotionally obtuse, which lends to their overall wariness about each other. While Doctor may be more open with Amiya, Kal has seen a side of Doctor that no one else has, and that sort of knowledge is strange and unsettling, even frightening. Kal will forever hold it against Doctor, despite them "not being the same person as before" due to their amnesia. But to what extent does a past action define someone? If they don't recall it? And to what degree does them wanting to reclaim their identity means a reason to be concerned?

My Doctor feels alienated and isolated, but also because they have a desire to become "whole" again, and that involves going back to Priestess, despite all signs pointing to how sinister she is and how little she seems to care about Terra. The dynamic between KalDoc becomes a lot more intriguing when you have to tackle the concept of identity, and how (my) Doctor has to reconcile being a good person while also reaping the consequences of their own actions, and yet feeling an emptiness that cannot be filled nor alleviated in any way without returning to what made them a monster in the eyes of others.

The thing that makes KalDoc dynamics so precarious and difficult to get right and/or engaging is that you have to maintain Kal'tsit's resentment of Doctor without turning her into a tsundere. What makes it fascinating is that reducing it down to merely "hate" doesn't quite encapsulate all that feels, according to her. Hate isn't enough. It certainly isn't love, nor apathy. And Kal'tsit, while witnessing those glimmers of humanity from Doctor, cannot relinquish her resentment. She knows better to. Kal will protect Doctor, but will never fully trust nor forgive them. That resentment, that distrust, belongs to her. It will be the only thing that's hers. It's one of the many things that make her "Kal'tsit".

Also it's really, really hard to find queer female or nonbinary Doctor portrayals because 9 times out of 10 you'll trip across some rando who consistently uses he/him to refer to Doctor whenever they are paired with a female character. Or draws/writes them in a very stereotypical cishet male way. And while I know appearance doesn't necessarily dictate gender, and that nonbinary people can use he/him, I honestly doubt the wider gacha crowd is conscientious enough to consider a genuine NB depiction instead of just assuming that Doctor is a cishet man by default.

And thank you very much; if you enjoy those pairs, I encourage you to read the works by @dramaticgaze and @lykieu on Ao3. They are among my muses <3